Abstract :
We study certain Poincaré-type series on the generalized Jacobi group image (Hg(image = generalized Heisenberg group) which depend on two parameters δ > 0 and s set membership, variant image, Re(s) much greater-than 0. Using the theory of Eisenstein series on Spg + 1(image), it is shown that they have a meromorphic continuation to the s-plane and satisfy a certain functional equation; moreover, in the limiting case δ → ∞ one obtains a classical Eisenstein series on GJ. Finally, it is proved that if one applies the Rankin-Selberg method with the above series, one obtains up to a Whittaker function a (generalized) Mellin transform of a constant term as familiar from the usual theory of Eisenstein series.
